As stated earlier, the quickest way to fix this is to VLAN in your administrative subnet via one of your Ethernet interfaces - this not only provides you the interface you need to reach your SMTP gateway for AutoSupport, it will also give you a fully functional management interface for Telnet/SSH, FilerView, etc.
I also wanted to clarify what the BMC does w.r.t. AutoSupport transmissions. The BMC sends a very small subset of AutoSupport message events - they are ones that are considered severe in nature (system is down, abnormally rebooted). The BMC does NOT act as any kind of proxy for AutoSupport messages originating from the system itself.
As stated earlier, the BMC reads the AutoSupport configuration information (options) from its host system. Therefore, as you have things configured right now, the BMC is capable of sending that subset of severe AutoSupport messages. You can test that via the BMC CLI, if you like.
However, if you'd like to get full automation from AutoSupport and corresponding usage of the My AutoSupport portal, you'll need to provide that IP path via an administrative interfaces (VLAN'ed, if you like).
Regards,
-Andris